Question 41

If $$(x+\frac{1}{x})^2=3$$, then the value of $$x^3+\frac{1}{x^3}$$ is

Solution

Expression : $$(x+\frac{1}{x})^2=3$$

=> $$(x+\frac{1}{x})=\sqrt3$$ ------------(i)

Cubing both sides, we get :

=> $$(x+\frac{1}{x})^3=(\sqrt3)^3$$

=> $$x^3+\frac{1}{x^3}+3(x)(\frac{1}{x})(x+\frac{1}{x})=3\sqrt3$$

Substituting value of $$(x+\frac{1}{x})$$ from equation (i)

=> $$x^3+\frac{1}{x^3}+3\sqrt3=3\sqrt3$$

=> $$x^3+\frac{1}{x^3}=0$$

=> Ans - (A)

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